Filter bank based fractional delay filter implementation for widely accurate broadband steering vectors

Applications such as broadband angle of arrival estimation require the implementation of accurate broadband steering vectors, which generally rely on fractional delay filter designs. These designs commonly exhibit a rapidly decreasing performance as the Nyquist rate is approached. To overcome this, we propose a filter bank based approach, where standard fractional delay filters operate on a series of frequency-shifted oversampled subband signals, such that they appear in the filter's lowpass region. Simulations demonstrate the appeal of this approach

Asynchronous Representation and Processing of Analog Sparse Signals Using a Time-Scale Framework

In this dissertation we investigate the problem of asynchronous representation and processing of analog sparse signals using a time-scale framework. Recently, in the design of signal representations the focus has been on the use of application-driven constraints for optimality purposes. Appearing in many fields such as neuroscience, implantable biomedical diagnostic devices, and sensor network applications, sparse or burst--like signals are of great interest. A common challenge in the representation of such signals is that they exhibit non--stationary behavior with frequency--varying spectra. By ignoring that the maximum frequency of their spectra is changing with time, uniformly sampling sparse signals collects samples in quiescent segments and results in high power dissipation. Also, continuous monitoring of signals challenges data acquisition, storage, and processing; especially if remote monitoring is desired, as this would require that a large number of samples be generated, stored and transmitted. Power consumption and the type of processing imposed by the size of the devices in the aforementioned applications has motivated the use of asynchronous approaches in our research. First, we work on establishing a new paradigm for the representation of analog sparse signals using a time-frequency representation. Second, we develop a scale-based signal decomposition framework which uses filter-bank structures for the representation-analysis-compression scheme of the sparse information. Using an asynchronous signal decomposition scheme leads to reduced computational requirements and lower power consumption; thus it is promising for hardware implementation. In addition, the proposed algorithm does not require prior knowledge of the bandwidth of the signal and the effect of noise can still be alleviated. Finally, we consider the synthesis step, where the target signal is reconstructed from compressed data. We implement a perfect reconstruction filter bank based on Slepian wavelets to use in the reconstruction of sparse signals from non--uniform samples. In this work, experiments on primary biomedical signal applications, such as electrocardiogram (EEG), swallowing signals and heart sound recordings have achieved significant improvements over traditional methods in the sensing and processing of sparse data. The results are also promising in applications including compression and denoising

On causal extrapolation of sequences with applications to forecasting

The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for forecasting. This lead to a forecasting method for more general sequences without this feature based on minimization of the mean square error between the observed path and a predicable sequence. These procedure involves calculation of this predictable path; the procedure can be interpreted as causal smoothing. The corresponding smoothed sequences allow unique extrapolations to future times that can be interpreted as optimal forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670

Applications of Continuous Spatial Models in Multiple Antenna Signal Processing

This thesis covers the investigation and application of continuous spatial models for multiple antenna signal processing. The use of antenna arrays for advanced sensing and communications systems has been facilitated by the rapid increase in the capabilities of digital signal processing systems. The wireless communications channel will vary across space as different signal paths from the same source combine and interfere. This creates a level of spatial diversity that can be exploited to improve the robustness and overall capacity of the wireless channel. Conventional approaches to using spatial diversity have centered on smart, adaptive antennas and spatial beam forming. Recently, the more general theory of multiple input, multiple output (MIMO) systems has been developed to utilise the independent spatial communication modes offered in a scattering environment. ¶ ..

Quantum lattice models that preserve continuous translation symmetry

Bandlimited approaches to quantum field theory offer the tantalizing possibility of working with fields that are simultaneously both continuous and discrete via the Shannon Sampling Theorem from signal processing. Conflicting assumptions in general relativity and quantum field theory motivate the use of such an appealing analytical tool that could thread the needle to meet both requirements. Bandlimited continuous quantum fields are isomorphic to lattice theories, yet without requiring a fixed lattice. Any lattice with a required minimum spacing can be used. This is an isomorphism that avoids taking the limit of the lattice spacing going to zero. In this work, we explore the consequences of this isomorphism, including the emergence of effectively continuous symmetries in quantum lattice theories. One obtains conserved lattice observables for these continuous symmetries, as well as a duality of locality from the two perspectives. We expect this work and its extensions to provide useful tools for considering numerical lattice models of continuous quantum fields arising from the availability of discreteness without a fixed lattice, as well as offering new insights into emergent continuous symmetries in lattice models and possible laboratory demonstrations of these phenomena.Comment: 16 pages, 5 figure

A Stochastic Modeling Approach to Region-and Edge-Based Image Segmentation

The purpose of image segmentation is to isolate objects in a scene from the background. This is a very important step in any computer vision system since various tasks, such as shape analysis and object recognition, require accurate image segmentation. Image segmentation can also produce tremendous data reduction. Edge-based and region-based segmentation have been examined and two new algorithms based on recent results in random field theory have been developed. The edge-based segmentation algorithm uses the pixel gray level intensity information to allocate object boundaries in two stages: edge enhancement, followed by edge linking. Edge enhancement is accomplished by maximum energy filters used in one-dimensional bandlimited signal analysis. The issue of optimum filter spatial support is analyzed for ideal edge models. Edge linking is performed by quantitative sequential search using the Stack algorithm. Two probabilistic search metrics are introduced and their optimality is proven and demonstrated on test as well as real scenes. Compared to other methods, this algorithm is shown to produce more accurate allocation of object boundaries. Region-based segmentation was modeled as a MAP estimation problem in which the actual (unknown) objects were estimated from the observed (known) image by a recursive classification algorithms. The observed image was modeled by an Autoregressive (AR) model whose parameters were estimated locally, and a Gibbs-Markov random field (GMRF) model was used to model the unknown scene. A computational study was conducted on images having various types of texture images. The issues of parameter estimation, neighborhood selection, and model orders were examined. It is concluded that the MAP approach for region segmentation generally works well on images having a large content of microtextures which can be properly modeled by both AR and GMRF models. On these texture images, second order AR and GMRF models were shown to be adequate

Roadmap on Superoscillations

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments